Energy firms will be banned from charging catch-up bills for gas and electricity used more than 12 months earlier.
Regulator Ofgem's new rule, to start in May for domestic customers, should stop shock bills of thousands of pounds.
Customers who pay via direct debit often receive bills based on estimated meter readings.
When an actual reading is taken, the supplier "back-bills" the customer for any shortfall.
Other supposed arrears have occurred as a result of errors in suppliers' billing systems.
Ofgem said the typical back bill was £1,160 and in extreme cases they have exceeded £10,000. Most customers struggle to pay and some are driven into debt. The regulator said it was aware of 10,000 complaints in a year.
The ban will start in May for domestic customers and in November for the smallest businesses. The only exception is when customers have purposefully prevented the company from taking a reading.
A voluntary agreement to stop back-billing of more than 12 months has been in place among the biggest suppliers since 2007. However, some have not fully complied and smaller firms were not signed up.
"Getting billing right is an essential part of customer service, and it's unfair that consumers should be left out of pocket when through no fault of their own they're issued with a shock bill from their supplier," said Rob Salter-Church, from Ofgem.
Victoria MacGregor, director of energy at Citizens Advice, said: "We have long called for the changes announced today. The new rules will deliver better protections for households and small businesses across the country. No-one should face a massive unforeseen bill that goes back years when it is their supplier that is at fault.
"Previously we've seen evidence of suppliers trying to game the rules by blaming customers for billing errors, cases where suppliers have ignored their commitments entirely, and small businesses receiving unexpected bills running to tens of thousands of pounds."
Lawrence Slade, chief executive of Energy UK said: "Energy companies take accurate billing very seriously and where there are problems, the majority are resolved within 24 hours.
"Suppliers are actively working to improve billing for their customers. That is why companies covering 80% of the market have signed up to the Energy UK Billing Code to ensure greater accuracy of bills. Audit results of the code show year-on-year improvement and complaint numbers are falling."